查看更多>>摘要：This paper aims to develop a direct approach,namely,the Cauchy matrix approach,to non-isospectral integrable systems.In the Cauchy matrix approach,the Sylvester equation plays a central role,which defines a dressed Cauchy matrix to provide τ functions for the investigated equations.In this paper,using the Cauchy matrix approach,we derive three non-isospectral nonlinear Schrödinger equations and their explicit solutions.These equations are generically related to the time-dependent spectral parameter in the Zakharov-Shabat-Ablowitz-Kaup-Newell-Segur spectral problem.Their solutions are obtained from the solutions of unreduced non-isospectral nonlinear Schrödinger equations through complex reduction.These solutions are analyzed and illustrated to show the non-isospectral effects in dynamics of solitons.
查看更多>>摘要：The integer-order interdependent calcium([Ca2+])and nitric oxide(NO)systems are unable to shed light on the influences of the superdiffusion and memory in triggering Brownian motion(BM)in neurons.Therefore,a mathematical model is constructed for the fractional-order nonlinear spatiotemporal systems of[Ca2+]and NO incorporating reaction-diffusion equations in neurons.The two-way feedback process between[Ca2+]and NO systems through calcium feedback on NO production and NO feedback on calcium through cyclic guanosine monophosphate(cGMP)with plasmalemmal[Ca2+]-ATPase(PMCA)was incorporated in the model.The Crank-Nicholson scheme(CNS)with Grunwald approximation along spatial derivatives and L1 scheme along temporal derivatives with Gauss-Seidel(GS)iterations were employed.The numerical outcomes were analyzed to get insights into superdiffusion,buffer,and memory exhibiting BM of[Ca2+]and NO systems.The conditions,events and mechanisms leading to dysfunctions in calcium and NO systems and causing different diseases like Parkinson's were explored in neurons.
查看更多>>摘要：In this paper,by using the Darboux transformation(DT)method and the Taylor expansion method,a new nth-order determinant of the hybrid rogue waves and breathers solution on the double-periodic background of the Kundu-DNLS equation is constructed when n is even.Breathers and rogue waves can be obtained from this determinant,respectively.Further to this,the hybrid rogue waves and breathers solutions on the different periodic backgrounds are given explicitly,including the single-periodic background,the double-periodic background and the plane wave background by selecting different parameters.In addition,the form of the obtained solutions is summarized.
查看更多>>摘要：In this paper,two different methods for calculating the conservation laws are used,these are the direct construction of conservation laws and the conservation theorem proposed by Ibragimov.Using these two methods,we obtain the conservation laws of the Gardner equation,Landau-Ginzburg-Higgs equation and Hirota-Satsuma equation,respectively.
Haifa A AlyousefAlvaro H SalasB M AlotaibiS A El-Tantawy...
58-67页
查看更多>>摘要：This study reports the analytical solution for a generalized rotational pendulum system with gallows and periodic excited forces.The multiple scales method(MSM)is applied to solve the proposed problem.Several types of rotational pendulum oscillators are studied and talked about in detail.These include the forced damped rotating pendulum oscillator with gallows,the damped standard simple pendulum oscillator,and the damped rotating pendulum oscillator without gallows.The MSM first-order approximations for all the cases mentioned are derived in detail.The obtained results are illustrated with concrete numerical examples.The first-order MSM approximations are compared to the fourth-order Runge-Kutta(RK4)numerical approximations.Additionally,the maximum error is estimated for the first-order approximations obtained through the MSM,compared to the numerical approximations obtained by the RK4 method.Furthermore,we conducted a comparative analysis of the outcomes obtained by the used method(MSM)and He-MSM to ascertain their respective levels of precision.The proposed method can be applied to analyze many strong nonlinear oscillatory equations.
查看更多>>摘要：Neural networks possess formidable representational power,rendering them invaluable in solving complex quantum many-body systems.While they excel at analyzing static solutions,nonequilibrium processes,including critical dynamics during a quantum phase transition,pose a greater challenge for neural networks.To address this,we utilize neural networks and machine learning algorithms to investigate time evolutions,universal statistics,and correlations of topological defects in a one-dimensional transverse-field quantum Ising model.Specifically,our analysis involves computing the energy of the system during a quantum phase transition following a linear quench of the transverse magnetic field strength.The excitation energies satisfy a power-law relation to the quench rate,indicating a proportional relationship between the excitation energy and the kink numbers.Moreover,we establish a universal power-law relationship between the first three cumulants of the kink numbers and the quench rate,indicating a binomial distribution of the kinks.Finally,the normalized kink-kink correlations are also investigated and it is found that the numerical values are consistent with the analytic formula.
查看更多>>摘要：We propose a theoretical scheme to realize a two-dimensional(2D)diffraction grating in a four-level in verted-Y-type atomic system coupled by a standing-wave(SW)field and a Laguerre-Gaussian(LG)vortex field.Owing to asymmetric spatial modulation of the LG vortex field,the incident probe field can be lopsidedly diffracted into four domains and an asymmetric 2D electromagnetically induced grating is created.By adjusting the detunings of the probe field and the LG vortex field,the intensities of the LG vortex field and the coherent SW field,as well as the interaction length,the diffraction properties and efficiency,can be effectively manipulated.In addition,the effect of the azimuthal parameter on the Fraunhofer diffraction of the probe field is also discussed.This asymmetric 2D diffraction grating scheme may provide a versatile platform for designing quantum devices that require asymmetric light transmission.
查看更多>>摘要：The fusion barriers and cross sections of 15 colliding systems with 320 ≤Z1Z2≤1512 are investigated in detail to understand the influence of the universal function of proximity potential formalism in the heavy-ion fusion mechanism.To realize this goal,we select three versions of the phenomenological proximity potentials,including Prox.77,Zhang 2013,and Guo 2013,to calculate the nucleus-nucleus potential.The experimental fusion cross sections for the selected reactions are analyzed using the standard coupled-channel calculations,including couplings to the low-lying 2+and 3-states in the target and projectile.The calculated results show that the universal functions of the Guo 2013 and Prox.77 models provide the lowest and highest fusion barriers,respectively.In addition,it is found that the height of the fusion barriers is enhanced by increasing the mass number of the projectile from light to heavy ones.The highest sensitivity to the mass number of the projectile belongs to the results of Prox.77.A discussion is also presented on the influence of the universal function on the radial behavior of the interaction potential in the allowed region for overlapping configurations.Our results reveal that the best fit to the experimental data of the fusion cross sections for the reactions involving light and medium nuclei is obtained using the universal function of the Zhang 2013 model.For the heavier systems,the results of the Guo 2013 model at sub-barrier energies provide a good description of the available data.
查看更多>>摘要：Using N=2 supergravity formalism,we investigate certain behaviors of five-dimensional black objects from the compactification of M-theory on a Calabi-Yau three-fold.The manifold has been constructed as the intersection of two homogeneous polynomials of degrees(ω+2,1)and(2,1)in a product of two weighted projective spaces given by (WP)4(ω,1,1,1,1)×(P)1.First,we determine the allowed electric charge regions of the BPS and non BPS black holes obtained by wrapping M2-branes on appropriate two cycles in such a proposed Calabi-Yau three-fold.After that,we calculate the entropy of these solutions which takes a maximal value corresponding to ω=1 defining the ordinary projective space (P)4.For generic values of ω,we show that the non BPS states are unstable.Then,we conduct a similar study of five-dimensional black strings.Concerning the allowed magnetic charge regions of the BPS and non BPS black stringy solutions derived from M5-branes on dual divisors,we calculate the tension taking a minimal value for (P)4.By determining the recombination factor,we show that the non-BPS black string states are stable in the allowed regions in the magnetic charge space.
查看更多>>摘要：In the background of f(R,Lm)gravity,this work investigates three distinct dark matter halo profiles to test the possibility of generalised wormhole geometry within the galactic halo regions.The current study aims to accomplish these goals by examining various dark matter profiles including universal rotation curves(URC),Navarro-Frenk-White(NFW)model-Ⅰ,and NFW model-Ⅱ inside two distinct f(R,Lm)gravity models.According to the f(R,Lm)=R/2+Lαm model,the dark matter(DM)halo density profiles produce suitable shape functions that meet all the necessary requirements for exhibiting the wormhole geometries with appropriate choice of free parameters.In addition,to examine DM profiles under the f(R,Lm)=R/2+(1+λR)Lm model,we consider a specific shape function.Further,we observed that the derived solution from both two models violates the null energy constraints,confirming that the DM supports wormholes to maintain in the galactic halo.
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